CS 175: Topics in Geometric Modeling
 

Homework Assignments


Assignment 8, due 06-03-03, 11:59pm

In this assignment you will compute a parameterization for a mesh with boundary.  To do so, you will constrain the boundary to the unit disc, and solve a sparse linear system to compute parameter values for the vertices on the mesh interior.  We will look at four of the parameterization schemes discussed in class: uniform, chord length, conformal, and mean value.

The parameterization algorithm is comprised of three steps:

  1. constraining the boundary vertices to the unit disc;
  2. computing the matrix coefficients for the interior vertices;
  3. solving the resulting sparse linear system using the conjugate gradient method.

For the first step, you will modify the code in the parameterization method to parameterize the boundary vertices by chord-length.  In the second step, the rows of the matrix which correspond to the interior vertices are defined by calling the method corresponding to the chosen parameterization scheme.  The uniform parameterization has been provided as an example.  Your task is to compute the coefficients for the other three parameterization schemes.  For the third step, you must implement a conjugate gradient solver using the matrix-vector multiplication function provided.  The method is described here on page 38.  Iterate until the magnitude of the residual rTr falls below some reasonable thresold, eg. 10-3.  For your final submission, include an ASCII file that records the number of iterations required to compute each parameterization of the face model.

Project files

Sample data files:

 

Copyright © 2003 Kai Hormann and Nathan Litke